IB Chemistry HL: pH Titration Curve Analysis | IB化学HL：pH滴定曲线分析

📚 IB Chemistry HL: pH Titration Curve Analysis | IB化学HL：pH滴定曲线分析

A pH titration curve is a graph of pH against the volume of titrant (the solution of known concentration) added from a burette. In IB Chemistry HL, the ability to interpret and sketch these curves is a fundamental skill, as it reveals the acid-base nature of the species involved, buffer regions, and the equivalence point. This article systematically analyses each type of titration curve, the calculations at key points, and how to select an appropriate indicator.

pH滴定曲线是加入滴定剂（已知浓度的溶液）的体积与溶液的pH值之间的关系图。在IB化学HL中，解读和绘制这些曲线是一项基本技能，因为它能揭示所涉及物种的酸碱性质、缓冲区域和等当点。本文系统分析各类滴定曲线、关键点处的计算以及如何选择合适的指示剂。

1. The Shape and Meaning of a Titration Curve | 滴定曲线的形状与意义

The x-axis records the volume of titrant added, while the y-axis shows the pH of the analyte solution. Each type of acid-base titration produces a characteristic curve. The steep vertical section indicates the equivalence point, where the acid and base have reacted completely. The midpoint of the vertical section is the equivalence point; before and after it, the pH changes are gradual. The inflection point of the curve corresponds to the maximum rate of change of pH.

横轴记录加入滴定剂的体积，纵轴显示被分析溶液的pH值。每种类型的酸碱滴定都会产生特征曲线。陡峭的垂直段表示等当点，即酸碱完全反应的点。垂直段的中点是等当点；在此之前和之后，pH变化是逐渐的。曲线的拐点对应pH变化速率最大的位置。

2. Key Terms: Equivalence Point, Half-Equivalence, Endpoint | 关键术语：等当点、半等当点、终点

• Equivalence point: the point at which the moles of H⁺ from the acid equal the moles of OH⁻ from the base, i.e. stoichiometric completion.

  等当点：酸提供的H⁺的物质的量等于碱提供的OH⁻的物质的量，即按化学计量完全反应的点。

• Half-equivalence point: the point at which half of the acid (or base) has been neutralized; for a weak acid, [HA] = [A⁻] and pH = pKa.

  半等当点：一半的酸（或碱）已被中和的点；对于弱酸，[HA] = [A⁻]，pH = pKa。

• Endpoint: the point where the indicator changes colour; it should be as close as possible to the equivalence point.

  终点：指示剂变色的点；应尽可能接近等当点。

• Buffer region: the portion of the curve where pH changes very little upon addition of titrant, typically around the half-equivalence point.

  缓冲区域：曲线中加入少量滴定剂时pH几乎不变的区域，通常在半等当点附近。

3. Strong Acid – Strong Base Titration | 强酸-强碱滴定

For example, 0.100 mol dm⁻³ HCl titrated with 0.100 mol dm⁻³ NaOH. The initial pH is 1.00. As NaOH is added, the pH rises slowly at first, then jumps sharply from about pH 3 to pH 11 near the equivalence point. The equivalence point occurs at pH 7 because the resulting salt, NaCl, does not hydrolyse.

例如，用0.100 mol dm⁻³的NaOH滴定0.100 mol dm⁻³的HCl。初始pH为1.00。加入NaOH后，pH先缓慢上升，然后在等当点附近从约pH 3急剧跳到pH 11。等当点的pH为7，因为生成的盐NaCl不发生水解。

The vertical jump is large, typically from pH 3 to pH 11, so indicators such as methyl orange, bromothymol blue and phenolphthalein all give satisfactory endpoints. The exact volume of base needed at the equivalence point is calculated from the stoichiometric equation.

垂直跳跃很大，通常从pH 3到pH 11，因此甲基橙、溴百里酚蓝和酚酞等指示剂都能给出满意的终点。等当点所需的碱的准确体积由化学计量方程计算得出。

4. Weak Acid – Strong Base Titration | 弱酸-强碱滴定

Consider 0.100 mol dm⁻³ ethanoic acid (CH₃COOH, Ka = 1.8 × 10⁻⁵) titrated with 0.100 mol dm⁻³ NaOH. The initial pH is higher than that of a strong acid of the same concentration because the acid is only partially dissociated. Before the equivalence point, a buffer solution of CH₃COOH and CH₃COO⁻ forms, flattening the curve.

考虑用0.100 mol dm⁻³ NaOH滴定0.100 mol dm⁻³乙酸（CH₃COOH，Ka = 1.8 × 10⁻⁵）。由于酸仅部分电离，初始pH比同浓度强酸高。在等当点之前，CH₃COOH和CH₃COO⁻形成缓冲溶液，使曲线趋于平缓。

At half-equivalence, pH = pKa ≈ 4.74. At the equivalence point, the solution contains CH₃COO⁻, a weak base, so pH > 7 (typically about 8.7 for 0.05 mol dm⁻³ sodium ethanoate). The vertical section is shorter than for a strong acid-strong base titration, because the pH jump spans a narrower range.

在半等当点，pH = pKa ≈ 4.74。在等当点，溶液含有弱碱CH₃COO⁻，因此pH > 7（对于0.05 mol dm⁻³乙酸钠，通常约为8.7）。垂直段比强酸-强碱滴定短，因为pH跳跃覆盖的范围更窄。

5. Weak Base – Strong Acid Titration | 弱碱-强酸滴定

Example: 0.100 mol dm⁻³ ammonia solution (NH₃, Kb = 1.8 × 10⁻⁵) titrated with HCl. The initial pH is about 11.1. The curve falls gradually, with a buffer region around pH = 9.25 (half-equivalence where [NH₃] = [NH₄⁺]). At the equivalence point, the solution contains NH₄⁺, a weak acid, so pH < 7 (around 5.3). The steep section is shorter than for a strong acid and strong base.

例如：用HCl滴定0.100 mol dm⁻³氨水（NH₃，Kb = 1.8 × 10⁻⁵）。初始pH约为11.1。曲线逐渐下降，在pH ≈ 9.25处出现缓冲区域（半等当点，[NH₃] = [NH₄⁺]）。在等当点，溶液含有弱酸NH₄⁺，因此pH < 7（约5.3）。陡峭段比强酸-强碱短。

For this system, the half-equivalence pH can be related to pKb or to the pKa of the conjugate acid NH₄⁺. Since pKa + pKb = 14, the half-equivalence pH equals 14 − pKb.

对于该体系，半等当点pH可与pKb或共轭酸NH₄⁺的pKa联系。由于pKa + pKb = 14，半等当点pH等于14 − pKb。

6. Polyprotic Acid Titration | 多元酸滴定

Polyprotic acids such as H₃PO₄ release protons in steps, giving multiple equivalence points. For H₃PO₄, the curve has two clear endpoints (for the first two protons) and a third that is less distinct. Each buffer region corresponds to one acid-conjugate base pair, and the pH at each half-equivalence equals the relevant pKa: pKa1 ≈ 2.15, pKa2 ≈ 7.20, pKa3 ≈ 12.35.

像H₃PO₄这样的多元酸分步释放质子，产生多个等当点。对于H₃PO₄，曲线有两个清晰的终点（对应前两个质子），第三个终点不太明显。每个缓冲区域对应一对酸-共轭碱，每个半等当点的pH等于相应的pKa：pKa1 ≈ 2.15，pKa2 ≈ 7.20，pKa3 ≈ 12.35。

When titrating a diprotic acid such as H₂CO₃, the first equivalence point corresponds to the formation of HCO₃⁻, and the second to CO₃²⁻. The number of moles of base required for each step is equal, so the volume between consecutive equivalence points is the same

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